2000 Toyota Camry CE 4cyl

As near as I can tell it does sound like the thermostat is stuck closed. Coolant will not flow through it. If the hot coolant can't reach the temperature switch the fan won't turn on either.

You mentioned that no water was flowing through the upper radiator hose when the engine temperature was real high. That says the thermostat is not opening. Is it possible you put it in upside-down? Or could the gasket have laid over it and is blocking it from opening?

You could also have a trapped air pocket under the thermostat. It will not open in the presence of hot air. The sensing element must be hit with hot coolant for it to open. Look near the housing for any threaded plug or temperature sensor on the engine side of the thermostat, not on the radiator hose side. Remove anything that will let the air come out as you continue to fill the radiator.

Look at your old thermostat to see if there is a tiny bleed hole in it, usually with a little weight swinging in it. That is to help the coolant flow from where it is already hot to the thermostat to get the heat to it faster. That bleed hole also helps the trapped air get out and go to the radiator. Many new thermostats don't have that bleed hole. Drilling a 1/16" hole in it solved that problem on my van.

Yes, it's necessary. After working perfectly fine for years, my '88 Grand Caravan suddenly developed a problem where after driving about five miles on the highway, the temperature gauge would go almost to maximum, sit there a few seconds, then drop down to cold and slowly come back up. It would do that three or four times before it finally smoothed out and stayed in the normal range. It did that for months. It dropped to cold when the thermostat finally opened and cold coolant came rushing in from the radiator. That would cause the thermostat to close again. Finally I had one of my students take the thermostat out and I drilled a 1/16" hole in it. That solved the problem, and today, about five years later, it is still working fine.

The reason for the wide range of fluctuation is the sensor for the gauge on the dash is not real close to the thermostat. It sees the rise in temperature long before that heat gets to the thermostat. With the bleed hole, the coolant can circulate very slowly before the thermostat opens. That allows the hot coolant to migrate over to the thermostat faster.

What you can try first instead of replacing the thermostat is to just remove it, then fill the radiator. When the coolant appears in the thermostat opening you can reinstall it and there will be very little trapped air behind it. The problem is though you will run into the same bleeding problem the next time the system is drained and refilled.

Can't say for sure but bleeder screws normally are in places where they are easy to see and access. A different plan of attack would be to connect a scanner that can display live sensor data to see what temperature the cooling system is running at. The electric radiator fan should turn on no higher than 210 degrees. Since the fan comes on and the temperature comes down when you select AC, it suggests the Engine Computer isn't seeing the correct temperature or it is not turning on the radiator fan relay.